I’m still not clear how to proceed
You need to make sure that both FM and EE use the same character encoding. I have a feeling that it might be easier to have EE use Latin-1 than teaching Unicode to FM.
So, go to Admin > System Preferences > General Configuration > Default Character Set and set it to iso-8859-1. Check that your template contains a line like this
<meta http-equiv="Content-Type" content="text/html; charset={charset}" />
Then post new articles, both via EE and by having FM do its thing.
The first is academic, but something I would like to understand for future reference: why does the wiki have instructions on hacking EE to use utf-8 when in my case it seems to be doing so by default?
You must distinguish between the encoding that is used in the control panel and your templates (utf-8 by default), and what is stored in the database (default depends on your database, the MySQL default is “latin1_swedish_ci”). The latter is usually irrelevant, as the encoding will be changed on the fly if needed. You can easily store UTF-8 encoded characters (or, really, any encoding) in a Latin-1 database. This is what EE does in 1.6.x. (EE 2.0 will have switched to utf-8 everywhere, including the database.)
Why the hack in the wiki? Because some user put it there. Under very rare circumstances this encoding will matter for the target system. Yours should not be one of these cases, however, so no hacks required.
The second is the one I need to resolve in order to follow your suggestion to give latin-1 a try: how do I get EE to do that, so that EE and FM are writing the same stuff to SQL, and sending the same stuff to the browser?
Change the default encoding as outlined above, and make sure that the correct “Content-Type” header appears in your templates.
what are the effects of all the variables shown in the EE SQL Manager, and how do I change them, if I need to? Screen shot from our CP attached, showing a worrying mix of the two charsets.
These are system variables used by MySQL to determine if and how to convert your data. You have changed some of them, it seems (collation_database and character_set_database, at a quick glance). Changing such variables is usually not sufficient since you’d also need to convert the data, but at the same time almost never necessary. Best to leave them alone.